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# Histogram Definition and Tutorial

Paired with a frequency distribution, the histogram offers investment analysts a picture of the variability of returns for an asset.
1. Define - Define Histogram charting for investments.
2. Context - Use Histogram in a sentence.
3. Video - See how it's done in Excel with a video.
4. Script - Follow along with the transcript below.
5. Quiz - Test yourself. by Paul Alan Davis, CFA
Updated: February 17, 2021
With a properly constructed histogram you can spot outliers that summary statistics hide. Keep reading.

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## Using Histogram of Returns for Investment Modeling

Beginner

Histogram is a chart showing the number, or frequency, of observations within ranges of data. Ranges may also be called buckets. The graphic, depicted using a bar chart, is helpful for identifying outliers and to validate that statistical tests are appropriate for the distribution of the data. A frequency distribution presents the same data in table form.

Synonym: frequency chart

A common mistake by investment modelers is to overly rely on summary statistics. It's easy to understand why. With thousands of stocks to review time is of the essence. Analysts find it most convenient to use the beta, standard deviation and correlation figures provided by their data service provider to arrive at a conclusion. The problem is that many risk measures utilize the mean, and the mean is subject to outliers.

One way to adjust for these biases is to visualize distributions using a histogram. In general, this is a good practice when making any decision based on statistical data.

### In a Sentence

Doc:  This histogram shows the distribution of past final grades in this Portfolio Theory class.
Leo:  Excuse me Professor, I have an unrelated question. What is the last day to drop?

### Video

This video can be accessed in a new window or App , at our YouTube Channel or from below.

Histogram definition for investment modeling (3:44)

### Video Script

The script includes two sections where we visualize and demonstrate the creation of a histogram.

#### Visualize

We're sitting right here in Excel and this is a snippet from our boot camp course.

First is the frequency distribution, followed by the histogram. Here we analyzed 60 monthly returns on four stocks, located on a tab called Returns and in this table we listed six ranges, or bins.

As an illustration, there were 9 returns of less than -10% for eBay and Merck had returns greater than 10%, 6 times.

The same data is presented graphically in a histogram. This visual perspective helps you spot errors and trends. It will also let you see if the distribution is in alignment with your statistical tests. See how eBay, in orange, had more observations away from the center, than Microsoft and Abbott Labs. So eBay would have higher risk if we measured it by standard deviation.

Next, let's demonstrate.

#### Demonstrate

There are eight steps to generate a frequency distribution and histogram in Excel.

The first seven are covered in another video on the frequency distribution, and because they go together, I will provide a link at the end of this video.

So our starting point here is the completed frequency distribution.

Highlight the range of data, including labels, click Insert, then Column. That's it. Of course, edit this histogram as you see fit.

Let's focus on the purpose of a histogram. For many statistical tests in investment modeling, even for studies with as few as 60 observations, it is common to use the normal distribution.

And a quick look at this indicates that more observations are in the tails, or away from the center, so it may make more sense to use a t-distribution instead of a normal distribution.

### Quiz

A histogram is useful for visualizing whether it is appropriate to use a normal distribution for statistical estimation. | True or False?

True

A histogram of returns typically utilizes a scatterplot in Excel. | True or False?

False. A vertical bar chart is most common.

Still unclear on the histogram? Leave a question in the comments section on YouTube or check out the Quant 101 Series, specifically Stock return frequency distributions and histograms in Excel.

### Related Terms

Our trained humans found other terms in the category statistics basics you may find helpful.

## What's Next?

• To see all terms in the Glossary, click Outline.
• For the calculation of Geometric Return, click Back.
• Keep the coffee and free content flowing, click Tip.
• To start thinking about timeframes and Historical Return, click Next.

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